Nuclear Motion in the σ‑Bound Regime of Metal−H2 Complexes:[Mg(H2)n=1−6]

2+

Brandon K. Mitchell and Ryan P. Steele*

Department of Chemistry and Henry Eyring Center for Theoretical Chemistry, Thatcher Building for Biological and BiophysicalChemistry, University of Utah, 315 S 1400 E, Salt Lake City, Utah 84112, United States

*S Supporting Information

ABSTRACT: The dynamic, quantum structure of [Mg(H2)n=1−6]2+complexes is

investigated via ab initio path integral molecular dynamics simulations. These complexesrepresent the strong, σ-complex regime of metal−H2 interactions and are representative ofbonding motifs found in metal−organic frameworks. Significant nuclear motion within thecoordination sphere is observed, even though the ligands remain largely intact. Quantumeffects are found to be important in the H−H and metal−H2 stretch coordinates, but theremaining motion in the molecule is well represented by classical simulations. Nearly freerotation of the dihydrogen moiety is observed in all complexes. Statistical averages anddistributions of structural parameters are found to deviate nontrivially from the sameparameters in static, equilibrium structures.

■ INTRODUCTION

The prediction1 and discovery2−9 of nonclassical dihydrogenligands (so-called σ complexes) in the early 1980s once againchallenged a chemist’s definition of a chemical bond. Ratherthan a canonical H−M−H dihydride bonding configuration, σ-H2 complexes exhibit an η2 bonding interaction between ametal center and the σ bond density of the nominally H2moiety. In the decades following these reports, numerousadditional examples of M−H2 complexes were discovered,10

including complexes with characteristics intermediate to thedihydride and σ complex regimes.11−32

Owing to this nonclassical three-center, two-electronbonding motif, theoretical and experimental studies havefrequently addressed the electronic factors governing theligand’s configuration.12−19,21,33−38 Electrostatics, as well asforward donation from the σ bond of the H2 ligand to a porbital of the metal center, provide a significant fraction of thedriving force for the roughly 15−20 kcal/mol of complexationenergy. Back-donation effects from an occupied d orbital of themetal to the empty σ* orbital of the H2 also dictate the positionof the complex on the sliding scale between dihydride and σ-complex configurations. Additional contributions from trans-ligand and cis-hydride effects provide further synthetic flexibilityin generating complexes with desired properties.This ability to tailor the binding strength and configuration

of the H2 unit has led to the use of dihydride/dihydrogencomplexes in an enormous variety of chemistry. The hydrideform has long been utilized in catalytic hydrogenation,39 whichis “perhaps the most important catalytic method in syntheticorganic chemistry”.40 Industrial applications often use aheterogeneous version of this process,41 whereas manysynthetic reactions, including recent successes in asymmetric

catalysis,42−46 employ homogeneous catalysts. At the other endof this family of bonding configurations, σ-complex interactionshave been shown to be useful in metal−organic frameworkmaterials for hydrogen storage applications.47−55 The compet-ing effects of forward- and back-donation, along with ligandeffects, have been used to tailor the binding energy of suchstorage systems.56,57

This report addresses nuclear motion in σ-H2 complexes,including the degree to which a static structure is viable and themanner in which zero-point energy and thermal motionsmodify the static picture. Inelastic neutron scattering experi-ments have used the inherent motion (or lack thereof) in suchcomplexes to infer the barrier heights to H2 rotation.

58−62 Infact, this nuclear motion was a key piece of evidence in thequantification of forward- and back-donation effects. Theforward donation is isotropic along the axis perpendicular tothe H2 bond, so any extant barrier is indicative of back-donation. Such a one-dimensional picture, however, is severelylimited and ignores the additional zero-point and thermalmotion in the remainder of the molecule, which will be shownto be significant in this work. Nuclear motion in dihydride andintermediate complexes remains an open question and will bethe focus of future studies, but this work analyzes the σ-complex limit of this family of compounds. In particular,nuclear motion in the series of [Mg(H2)n=1−6]

2+ complexes hasbeen analyzed via ab initio path integral simulation techniques.These compounds have been chosen because they fall squarelyin the σ-complex regime. The divalent magnesium cation

Received: May 19, 2014Revised: October 7, 2014Published: October 9, 2014

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provides a strong interaction with the H2 σ bond, whereas thelack of d orbital occupation prevents back-donation effects.Magnesium metal sites for hydrogen interaction are also ofinterest in metal−organic frameworks.47,56,63,64 Key questionsto be addressed include the fluxional nature of the structure ofthis complex, as well as the role of quantum mechanical zero-point motion in determining such properties.

■ METHODSComputational assessment of structural flexibility in metal−H2complexes requires an accurate treatment of the electronicstructure (which dictates the propensity and directionality ofbonding) as well as an accurate description of the quantummechanical nuclear motion. Ab initio path integral method-ology65−75 provides a route to tackling both halves of thisproblem. Path integral methods map a quantum particle ontoharmonically coupled, classical replicas of the system,colloquially referred to as a “ring polymer”, and generate apotentially exact representation of the quantum, thermalmotion. The spread and movement of the ring polymeraccount for quantum delocalization. Sampling via now-standardMonte Carlo (PIMC)66,68,75−77 or molecular dynamics(PIMD)73,78−80 algorithms provides an efficient route forcomputing the nonlocal excursions through configurationspace. When coupled with an electronic structure theory-based underlying potential energy surface, ab initio pathintegrals generate a first-principles and systematically improv-able approach to a fully quantum mechanical simulation of thesystem.In this work, second-order Møller−Plesset perturbation

theory81 within the resolution-of-the-identity approxima-tion82−88 (RI-MP2) was used as the underlying potentialmethod. As shown in Table S1 of the Supporting Information,the RI-MP2 method is consistent with coupled-clustertheory89,90 [CCSD and CCSD(T)] benchmarks for the bindingenergy of the H2 unit, structural parameters at equilibrium, andharmonic H2 stretch frequencies in the limiting cases of[Mg(H2)]

2+ and [Mg(H2)6]2+. The benchmarking results

demonstrate that the qualitative structure is consistent acrossall polarization function-containing basis sets. The cc-pVDZbasis set91,92 was chosen in this work as a reasonablecompromise of accuracy and the computational efficiencyrequired for configurational sampling. While the high-frequencyH−H harmonic stretch in [Mg(H2)]

2+ is overestimated in thismethod by 102 cm−1, the relative shift in frequency betweenbare H2 and the metal complex is well reproduced by RI-MP2/cc-pVDZ (423 cm−1) compared to large basis set CCSDbenchmarks (433 cm−1). Lower-frequency motions, such as theembedded H2 rotor motions, are moderately sensitive to thelevel of theory, but given the extremely low barriers to thismotion (see below), the resulting structural distributions arenot particularly sensitive to this quantity.The nuclear motion was simulated via the aforementioned

PIMD method at 300 K, and analogous classical simulationswere performed for comparison. The ring polymer consisted of32 system replicas in the PIMD simulations, which issufficiently converged for H-containing systems within thesecond-order Trotter expansion.93−97 A multiple-time-stepalgorithm80,98 for analytically propagating the ring polymernormal modes was employed within a velocity Verletintegrator,99 using a conservative time step of 0.25 fs and astochastic Langevin thermostat with a time constant of 1 ps forthe centroid motion. The PIMD results were sampled via 20

independent simulations of 100 000 steps (25 ps) each, exceptfor the [Mg(H2)6]

2+ complex, which was sampled with only50 000 steps (12.5 ps) for each trajectory. Analogous classicalMD simulations (1 system replica) were performed using thesame integration time step, thermostat parameter, andtrajectory length. This level of sampling was sufficient toreliably resolve the subtle structural changes that occur in thesecomplexes. All MD and PIMD calculations were performed inan MPI-based, parallel version of the Q-Chem 4.2 quantumchemistry software package.100 Analysis of statistical averages,distributions, and errors was performed via in-house routinesusing the Q-Chem results. Statistical errors in computedaverages were determined via a blocking analysis.101 Molecularstructures were generated with the VMD software package.102

■ RESULTS AND DISCUSSIONStatic and statistical structural information is presented in thefollowing section. Since the static structures of these complexeshave been reported previously,56 emphasis is placed on thestructural trends and the manner in which a dynamic picturemodifies the static structure.

Static Structure and Trends. The optimized equilibriumstructures of the [Mg(H2)n=1−6]

2+ complexes are shown inFigure 1 and are consistent with structures reported in previous

studies. All of the hydrogen units bind in an η2 fashion, and thefirst coordination sphere of the Mg2+ ion is completed at n = 6with an octahedral configuration. No appreciable attractionbetween the ligands is observed, as all complexes adoptconfigurations that maximize distance between neighboringligands. The lone exception to this maximization is complex 5,which exhibits a trigonal bipyramid structure. In all cases, slighttwisting of the dihydrogen ligands minimizes the subtleelectronic repulsions between them.Consistent with the energetic trends computed in the

benchmark results (Table S1 in Supporting Information), theH−H bond lengths indicate that the influence of the ion isdistributed across the H2 units and, therefore, diminishes on aper-H2 basis as the complex size increases. The single H2 ligandin [Mg(H2)]

2+ is moderately perturbed (rHH = 0.785 Å) relativeto bare dihydrogen (rHH = 0.754 Å), although the lengtheningis still well outside the realm of dihydride complexes. In the

Figure 1. Optimized equilibrium structures of [Mg(H2)n=1−6]2+ and

bare H2 using the RI-MP2/cc-pVDZ method. Shown are unique rHHand rMg−H bond lengths, in Å.

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case of complex 6, the six equivalent H−H bonds exhibitlengths intermediate to these two limiting cases, at rHH = 0.770Å. The Mg−H−H bond angle increases slightly, from 79.1° to79.7°, as the ligand sphere increases from 1 to 6, which isconsistent with the shortening H−H bond and the increasingdistance from the metal center to the H2 unit(s). Finally, thehydrogen ligands in [Mg(H2)6]

2+ are all oriented perpendicularto their nearest neighbors and parallel to the ligand oppositethe metal center. This symmetric structure minimizes ligandinteractions. All other structural details will be reserved formore substantive analysis in the context of nuclear motion inthe following subsection.Nuclear Motion. Analysis of the PIMD trajectories and

statistical data suggests that these complexes are notably morefluxional than a static structure implies. The followingdiscussion first examines the small complexes 1 and 2 in detail,in order to establish reference points and key structuralparameters, and then presents trends across all structuresthrough n = 6.[Mg(H2)]

2+. This triatomic species is reasonably limited inthe amount of internal motion possible, but it also highlightsstructural properties contained within the metal−H2 moietyalone. From the static structure calculations, complex 1 isknown to exhibit the strongest interaction between the metaland ligand. The average H−H bond length from the PIMDsimulations is ⟨rHH⟩ = 0.812 Å, which is nearly 0.03 Å longerthan the corresponding value in the static structure.Anharmonicity along the H−H stretch coordinate favors thislengthened bond and is apparent in the bond distributionshown in Figure 2. As expected, the quantum distribution forthis high-frequency motion is more than twice as broad as thedistribution from classical, thermal motion. The averagedistance from the metal center to the midpoint of the H−Hbond is ⟨rMg−H2

⟩ = 2.088 Å, which is also longer than the staticstructure value of 2.036 Å. These two quantities appear at oddswith one another, since a larger rMg−H2

value would make thedihydrogen ligand more H2-like and, therefore, exhibit a shorterrHH. The resolution of this apparent discrepancy is that thesecoordinates are all strongly coupled via interaction with themetal center, and some component of anharmonic Mg−Hstretch is involved in the admixture of H−H and Mg−H2.Tumbling/bending motion of the H2 ligand is also active.

While the average Mg−H−H angle (79.4°) is close to the staticvalue (79.1°), the breadth of the distribution indicates thatmotion ±40° from the minimum structure is active. A 5.6 kcal/mol barrier prevents complete rotation along this direction,however. Rotation of the ligand about the axis between themetal and the H2 bond midpoint is indistinguishable fromoverall rotation in complex 1, so discussion of this motion isreserved for the larger complexes. Overall, the quantumsimulations provide a structural picture in which anharmoniczero-point motion of the H−H stretch lengthens this bond andin which large-amplitude angular motion of the dihydrogenligand is active.[Mg(H2)2]

2+. Addition of a dihydrogen ligand to complex 1allows for examination of the relative motion of the ligands, aswell as the many-body effect of distributing the cation’sinfluence over multiple ligands. The static structure 2 possessesH2 ligands perpendicular to one another (dihedral angle ϕH2H2

= 90.6°). While the quantum, thermal average matches thisvalue, a single average value belies significantly active motion.The distribution of this dihedral angle is shown in the second

panel of Figure 3. Nearly free rotation is observed. (The biasaway from 0° and 180° is exacerbated by an angular distributionfactor rather than a true structural bias.) Computation of thehindered-rotor transition state at the same level of theoryexhibits a barrier of only 0.006 kcal/mol, which becomes −0.06kcal/mol upon inclusion of harmonic zero-point energy. Thisvanishing barrier is consistent with the absence of d back-bonding interactions and a concomitant lack of directionalpreference. Therefore, a more accurate depiction of thestructure along this coordinate is a magnesium cation flankedby two fully active hydrogen propellers. The quantum andclassical simulations produce very similar distributions along

Figure 2. Statistical structural distributions at 300 K for [Mg(H2)]2+

along three internal coordinates. Both classical MD and quantumPIMD distributions are depicted. In the top panel, the rHH bonddistribution for bare H2 is included for reference.

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this dihedral coordinate. While the low frequency of thismotion makes such a conclusion expected, the fact that thehigh-frequency dihydrogen stretches do not appreciably perturbthe distribution indicates that the coupling between these twodegrees of freedom is small.Interestingly, the average angle between the centers of the

ligands is found to be ⟨θMid−Mg−Mid = 136.4°⟩. The bendingmotion of the ligands, relative to each other, is active. Thisaverage value is biased somewhat by a subtle geometric factor;the linear arrangement is a single point in the H2−Mg−H2

configuration space, whereas nonlinear arrangements carve outa cone. Nonetheless, the distribution in the third panel ofFigure 3 demonstrates that bending motion is active overroughly 90°. The classical and quantum distributions exhibitnearly identical behavior; only the quantum distribution isshown in Figure 3.Comparison to complex 1 suggests that ⟨rHH⟩ is reduced in

complex 2 by roughly the same amount as in the staticstructure, even though the PIMD quantity (⟨rHH⟩ = 0.808 Å)remains notably longer than in the static reference structure.The qualitative shape of the curves in the first panel of Figure 3is nearly identical to the analogous plot in Figure 2. The anglebetween the metal center and the ligand bond is identical to theangle found for complex 2. The distance from the metal centerto the midpoint of the ligand is also only slightly lengthenedfrom its value in complex 1, although the lengthening is roughlydouble the change in the static structures. Therefore, the Mg−H2 unit alone appears consistent with the qualitative structurefound for 1, with the slightly shortened ligand and lengthenedmetal−ligand bond expected for the presence of two ligands.The relative motion of the two ligands is the unique feature ofthis complex. The low-frequency rotation and bending motionsare highly active and contribute to large-amplitude motion ofthe dihydrogen ligands.

[Mg(H2)3−6]2+. Additional dihydrogen ligands continue to

create nonclassical σ complexes, as shown in static structures3−6 of Figure 1. Remaining questions of structural flexibility inthese complexes include the attenuating influence of the metalon the H−H bond, as well as the manner in which additionalligands inhibit or exacerbate dihydrogen motion. Statisticallyaveraged structural values across the series of complexes areshown in Figure 4, with statistical distributions shown in Figure5.

Trends in Averaged Properties. The ⟨rHH⟩ values continueto decrease from complex 1 through complex 6, although theyremain notably longer than the rHH values for the staticstructures (also shown in Figure 4 for reference). Since roomtemperature excitation of this high-frequency motion isunlikely, the broad distribution and long average bond lengthare ascribed purely to anharmonicity. Such anharmonicity ismainly induced by the presence of the metal center, which isconfirmed by the fact that the same PIMD analysis applied tobare H2 only increases the bond length from a static value ofrHH = 0.754 Å to ⟨rHH⟩ = 0.779 Å.The average distance from the metal center to the midpoint

of the dihydrogen bond (rMg−H2) also increases as the number

of ligands increases. The source of this effect is the distributedinfluence of the metal cation over an increasing number ofligands. Since the ligand-dissociation coordinate becomes flatteras this effect occurs, the ligand can make larger anharmonicexcursions from the metal center. Accordingly, the relative gapbetween the static and quantum results also increases duringthe 1−6 progression.The averaged values of angular coordinates show trends

consistent with these changes in the dihydrogen ligands. As the⟨rMg−H2

⟩ distance increases, for example, the ⟨θH−Mg−H⟩ valuedecreases accordingly. The deviation of the averaged angularvalues from their static counterparts is small (although size-dependent), suggesting that this motion is reasonablyharmonic. The value for ⟨θH2−Mg−H2

⟩ in complex 2 suggestedthat relative bending motions of the ligands were active. Theaverages in Figure 4 indicate convergence toward the vicinity of

Figure 3. Statistical structural distributions at 300 K for [Mg(H2)2]2+

along three internal coordinates. Both classical MD and quantumPIMD distributions are depicted in the first two panels; classical andquantum results are nearly identical in the third panel. In the toppanel, the rHH bond distribution for bare H2 is again included forreference.

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the static average (over all angles) of 108°. However, thedistributions in the following section suggest that completeinhibition of bending does not occur. Finally, the dihedralangles between dihydrogen ligands remain near 90° throughoutthe complexes. That this value is observed over a range ofmolecular “shapes” in complexes 2−6 suggests that the ligandsare undergoing essentially unhindered rotation.Trends in Property Distributions. The distributions shown

in Figures 2 and 3 highlighted the large-amplitude motion forsmaller complexes, particularly in the H−H stretch and therelative motion of the ligands. Shown in Figure 5 are quantumdistributions across the series of compounds for the same

internal coordinates shown in Figure 4. The H−H bonddistribution shifts to shorter distances for larger complexes,although the width of the distribution remains roughlyconstant. The Mg−H2 bond distribution, however, lengthensand expands in width. This observation is consistent with thegrowing gap between static and dynamic values shown inFigure 4. The bending angular coordinates, θH−Mg−H andθMg−H−H, do not provide any new qualitative insight beyondtheir average values, although these plots do serve to quantifythe width of the distributions. The angular coordinatesdescribing relative motion of the ligands contain much moreinformation. The bending of the ligands relative to one another

Figure 4. Statistically averaged structural properties for complexes 1−6. In each case, both classical MD and quantum PIMD results are depicted, andin the left panels, static bond lengths are shown. In the first panel, results for H2 are also included. Error bars throughout are smaller than the symbolsin the plots, except for the lower-right panel, in which error bars are visible.

Figure 5. Quantum (PIMD) statistical distributions of structural properties for complexes 1−6. In the first panel, results for H2 are also included.

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was established as an active coordinate in complex 2. Thisdistribution shifts to smaller angles and eventually becomesbimodal for complexes 5 and 6, in accordance with the growingnumber of 90° angles in the latter compound’s static structure.The breadths of the two peaks indicate that the bending motionis, indeed, hindered in the more saturated complexes. Whereascomplex 2 was making large-amplitude motions between 180°and 90° configurations, the larger complexes exhibit lessbending flexibility due to the steric interactions withneighboring ligands. Finally, the dihedral distributions indicatethat the propeller-like motions of the ligands remain active inthe large complexes. Constrained potential energy scans alongthis rotor coordinate indicate that the motion of neighboringdihydrogen ligands is correlated, explaining the superimposedbroad and 90° peaks in the distribution.Given these structural trends, a reasonable question concerns

the experimental observation of such properties. Massspectrometry, as well as rotational and vibrational spectroscopy,of singly charged metal ions (ranging from Li+ to Cr+) boundto a dihydrogen ligands has been studied both experimen-tally103−107 and computationally.105,108,109 Backing structuralinformation out of these highly fluxional complexes ischallenging, although such theory−experiment studies holdpromise. These approaches should be extendable to thedivalent ions, with additional ligands, and such experimentalanalysis is encouraged here.Isomeric Flexibility. The static structures shown in Figure 1

were the only isomers that resulted from initial structuralsearches. The wealth of data from MD-based samplingprovided an opportunity to search for additional minimaaccessed by the trajectories, however. By use of these data forspecies 3−6, 2000 structures were extracted from the samplingand subsequently “quenched” via geometry optimizations,followed by harmonic vibrational analyses. In order to analyzethis large number of structures, rigid-body translation and(Euler angle) rotation were performed in order to optimallyalign the structures, using a root-mean-squared structuraldeviation (rmsd) as the optimization metric.While several previously unidentified first- and second-order

saddle points were discovered in this analysis, no energeticallyunique isomers were discovered. This result is consistent withthe lack of d orbital interactions between the metal cation andthe dihydrogen ligands; no spatial bias is imparted to theligands in order to form energetically distinct isomers. Animportant exception, however, is the discovery of energeticallyequivalent (but symmetrically inequivalent) structural isomers.Two n = 3 isomers, for example, are shown in Figure 6 assuperimposed, maximally aligned structures. In the originalisomer (white hydrogens), the dihydrogen ligands each cant ina consistent orientation, relative to the average plane of thecomplex. The new isomer (silver hydrogens) behaves in thesame fashion, but the hydrogens cant in the opposite direction.This change in angle can be obtained, physically, via internalrotation of the three ligands or, in the context of a symmetryanalysis, via mirror-image reflection in several possible planes.Interestingly, this molecule, therefore, possesses a “handed-ness”, which is qualitatively similar to known tris-(ethylenediamine) metal coordination complexes.110 It exhibitsa purely D3 point-group symmetry (not D3d or D3h). Similar H2-rotated isomers (not shown) were found in the largercomplexes 4−6.The MD/PIMD analyses, shown above, demonstrate that

such symmetry considerations are likely immaterial to an

understanding of the structure of this highly fluxional complex.The exquisitely low barriers to ligand rotation (as low as 0.01kcal/mol, obtained via the quenching search) lead tounhindered rotation of the ligands and a thermal/quantumaveraging of the resulting structures. The fact that energeticallyequivalent minima exist in these complexes is inherentlyconnected to this rotational flexibility, however.

Quantum vs Classical Motion. The path integralmethodology employed in this work provides a computationallytractable route for the potentially exact inclusion of quantummechanical nuclear motion, including zero-point effects,thermal motion, and tunneling. For this series of complexesin the limiting σ-bound regime, an analysis of the role of sucheffects is worthwhile. The H−H bond distribution is found tobe heavily quantum mechanical. Room-temperature thermalenergy in this degree of freedom is roughly an order ofmagnitude smaller than the zero-point energy, so such a resultwas anticipated. The in−out motion of the dihydrogen ligands,relative to the metal center, was also found to be appreciablyquantum mechanical. The remaining angular degrees offreedom, including the bending and propeller-like motions ofthe ligands, were all found to be suitably described by classicalmechanics. This latter result is expected if these low-frequencycoordinates are mostly decoupled from the more quantummechanical high-frequency motions. In this series of complexes,results indicate that this decoupling, to a large extent, doesoccur. Such a decoupling would not be expected, for example,in species intermediate to the dihydrogen and dihydride ligandregimes.

■ CONCLUSIONSAn analysis of the quantum mechanical motion of thecomplexes [Mg(H2)n=1−6]

2+ has been performed using on-the-fly ab initio path integral molecular dynamics techniques. Theresults of these simulations suggest a notably dynamicmolecular structure, which is qualitatively summarized inFigure 7 for two representative structures. The high-frequencyH−H stretch is found to possess a moderately broaddistribution, owing mainly to zero-point energy in ananharmonic potential. The bending motion of the dihydrogenligands relative to the metal center (and relative to oneanother) is active in all species. Similarly, the propeller-likerotation about the metal−ligand axis is also found to be active,generally undergoing nearly unhindered rotation.

Figure 6. Two unique structural isomers of complex 3 (viewedobliquely), which were obtained during the MD-based isomer search.The two structures (one visualized with darker hydrogen units) aremaximally aligned via rigid-body translations and rotations, using anrmsd-based metric.

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The role of such motions in influencing the binding (free)energies of these complexes has not yet been investigated. Theanharmonic zero-point contributions and entropic factors (dueto the active rotors) will putatively form the dominantdeviations from static, harmonic analyses. Such motionswould likely contribute nontrivially to metal−organic frame-work H2 storage capacities, for example. Analyses of thesefactors will be performed in subsequent studies.All of these low-frequency degrees of freedom exhibit large-

amplitude motion within the coordination sphere of thisstrongly bound complex. This ligand-sphere mobility is thebroader question to be addressed in dihydrogen, dihydride, andintermediate complexes, for which this study provides the firstin a series of representative analyses. In canonical dihydrides,the H2 bond is fully broken, whereas the M−H bond is strongerthan in dihydrogen complexes. In the current study, the H2bond is still reasonably intact (apart from slight, anharmonicperturbations from the metal), whereas the M−H2 bond isrelatively weaker. The latter property was shown clearly in theM−H2 bond averages and distributions of this work. Nohydride/proton shuttling between neighboring ligand sites wasobserved, suggesting that a highly dynamic structure consistingof intact H2 units is a reasonable qualitative picture of thecompounds’ structure. A remaining open question concerns theoptimal amount of intrasphere mobility for either H2 storage orhydrogenation catalysis purposes. This work has quantified thestructure of a series of species in the σ-complex limiting regimeand aims to serve as a useful reference point for futureexaminations of such mobility.

■ ASSOCIATED CONTENT

*S Supporting InformationBenchmark electronic structure parameters for complexes 1 and6. This material is available free of charge via the Internet athttp://pubs.acs.org.

■ AUTHOR INFORMATION

Corresponding Author*Phone: 801-587-3800. E-mail: ryan.steele@utah.edu.

NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTS

The support and resources from the Center for High-Performance Computing at the University of Utah aregratefully acknowledged. B.K.M. thanks Justin Talbot forhelpful discussions. R.P.S. acknowledges enlightening discus-sions with Prof. Michael Morse, as well as startup funds fromthe University of Utah.

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